PLT OF SMA RPTS NMAC WITH SECOND SMA WHEN ENTERING TFC PATTERN AT UNCTLED ARPT.

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#2 ACFT CHEROKEE LOW WING FIXED. I MONITORED UNICOM AND HEARD #2 PLT ANNOUNCING LOCATIONS AND INTENTIONS. I BROADCAST 'XING N TO S; MIDFIELD AT 8500 FT; DSNDING TO PATTERN ALT FOR 45 DEG ENTRY FOR L TFC RWY 24 PAYSON.' THE OTHER PLT REQUESTED MY LOCATION. I ADVISED '1/2 MI N OF RWY -- I HAVE YOUR ACFT UPWIND RWY 24.' I CROSSED THE RWY AND MUST HAVE BEGUN MY DSCNT AND I SAW THE OTHER ACFT WING UP XWIND TO DOWNWIND. AT APPROX 1/2 MI S OF THE RWY I SAW THE OTHER ACFT AT MY ALT WIDE ON DOWNWIND. I IMMEDIATELY DROPPED THE NOSE AND SLIPPED AGGRESSIVELY. THE OTHER ACFT PASSED OVERHEAD APPROX 300 FT. I RESUMED LEVEL FLT AND NOTED THAT I WAS AT APPROX 6100 FT. THE OTHER PLT ASKED MY LOCATION AND I ADVISED 'OFF YOUR WING.' OTHER PLT 'ARE YOU UNDER ME?' I ADVISED THAT I WAS TURNING TO A 45 DEG DOWNWIND ENTRY. BOTH PLANES THEN LANDED UNEVENTFULLY -- NO DISCUSSION. JUST PRIOR TO BEGINNING MY APCH TO PAYSON; I HAD OVERHEARD AN ALTIMETER SETTING AND WIND INFO. I DID NOT CHK MY ALTIMETER ON LNDG AT PAYSON BUT DID SO AT TAYLOR AND IT WAS ACCURATE WITHIN -75 FT WITHOUT ADJUSTMENT. I DO NOT FAULT THE OTHER PLT ALTHOUGH SHE MAY HAVE BEEN HIGH AND WIDE (TPA SHOWS 6200 FT). I MUST HAVE BEGAN DSCNT AND DONE SO AT A HIGH RATE BEFORE XING THE DOWNWIND PATTERN. I FEEL THAT HAD I NOT BEEN ABLE TO TAKE EVASIVE ACTION OR HAD NOT OBSERVED THE OTHER TFC IN MY SCAN WE WOULD HAVE COLLIDED.